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Part of 1984 Iran MO (2nd round)

Problems(1)

Prove that limits are equal - [Iran Second Round 1984]

Source:

12/30/2010
Let ff and gg be two functions such that f(x)=\frac{1}{\lfloor | x | \rfloor},   g(x)=\frac{1}{|\lfloor x \rfloor |}. Find the domains of ff and gg and then prove that lim⁡x→−1+f(x)=lim⁡x→1−g(x).\lim_{x \to -1^+} f(x)= \lim_{x \to 1^- } g(x).
functionfloor functionalgebradomainlimitalgebra unsolved